Microscale theory of surface tension

Antanovskiĭ, L. K.

doi:10.1103/physreve.54.6285

Cited by 58 publications

(56 citation statements)

References 17 publications

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“…In this theory, which further develops previous works by Antanovskii [13] and Español [14], the full set of thermo-hydrodynamic equations is derived for fluids with entropy and internal energy functionals including gradient terms. By assuming the usual expression for entropy production, a generalized Gibbs-Duhem relation taking into account the presence of interfaces was obtained.…”

Section: Introductionmentioning

confidence: 80%

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Dynamics of binary mixtures in inhomogeneous temperatures

Gonnella¹,

Lamura²,

Piscitelli³

2008

J. Phys. A: Math. Theor.

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A dynamical description for fluid binary mixtures with variable temperature and concentration gradient contributions to entropy and internal energy is given. By using mass, momentum and energy balance equations together with the standard expression for entropy production, a generalized GibbsDuhem relation is obtained which takes into account thermal and concentration gradient contributions. Then an expression for the pressure tensor is derived. As examples of applications, interface behavior and phase separation have been numerically studied in two dimensions neglecting the contributions of the velocity field. In the simplest case with a constant thermal gradient, the growth exponent for the averaged size of domains is found to have the usual value z = 1/3 and the domains appear elongated in the direction of the thermal gradient. When the system is quenched by contact with external walls, the evolution of temperature profiles in the system is shown and the domain morphology is characterized by interfaces perpendicular to the thermal gradient.

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Section: Introductionmentioning

confidence: 80%

“…By assuming the usual expression for entropy production, a generalized Gibbs-Duhem relation taking into account the presence of interfaces was obtained. This allowed us to get an expression for the pressure tensor containing explicit contributions resulting from thermal gradients, which did not appear in previous theories of [13,14].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of binary mixtures in inhomogeneous temperatures

Gonnella¹,

Lamura²,

Piscitelli³

2008

J. Phys. A: Math. Theor.

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“…We begin with the break up of a miscible drop in the IBA-water system. We will use here the model based on the Korteweg stresses which is derived to describe the motion of binary fluids [1], [2]. After that we use a simplified model in order to describe the evolution of the drop shape after the temperature increase (see Section 2.2).…”

Section: Simulations Of Miscible Dropsmentioning

confidence: 99%

“…There are various approaches to the derivation of the mathematical model describing capillary forces in miscible liquids (see [1], [2] and references therein). They start from the assumption that the free energy density depends on the square of the density gradient or of the composition gradient.…”

Section: Effective Interfacial Tension In Miscible Liquidsmentioning

confidence: 99%

Instabilities of Diffuse Interfaces

Bessonov

Viner

Volpert

et al. 2008

Math. Model. Nat. Phenom.

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Abstract. Composition gradients in miscible liquids can create volume forces resulting in various interfacial phenomena. Experimental observations of these phenomena are related to some difficulties because they are transient, sufficiently weak and can be hidden by gravity driven flows. As a consequence, the question about their existence and about adequate mathematical models is not yet completely elucidated. In this work we present some experimental evidences of interfacial phenomena in miscible liquids and numerical simulations of miscible drops and diffuse interfaces.

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“…Note that this and similar theories are often referred to as phase-field theories. Several groups use model-H to study the dynamics of fluids in the bulk or in a fixed confined geometry [1,35,19,2,41,28,42]. Recently, model-H was re-derived employing phenomenological non-equilibrium thermodynamics to consolidate a number of slightly differing formulations in the literature [40].…”

Section: Introductionmentioning

confidence: 99%

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

Fraštia

Thiele

Pismen

2010

Math. Model. Nat. Phenom.

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Abstract. We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem is numerically solved employing a Finite Element Method on an adaptive grid. The developed numerical scheme allows us to obtain the coupled steady-state film thickness profile and the concentration profile inside the film. As an example we determine steady state profiles for a reflection-symmetric twodimensional droplet for various surface tensions of the film and various preferential attraction strength of one component to the substrate. We discuss the relation of the results of the present diffuse interface theory to the sharp interface limit and determine the effective interface tension of the diffuse interface by several means.

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Microscale theory of surface tension

Cited by 58 publications

References 17 publications

Dynamics of binary mixtures in inhomogeneous temperatures

Dynamics of binary mixtures in inhomogeneous temperatures

Instabilities of Diffuse Interfaces

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

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